Gemara

12b - Mishnah: Tevu'ah and olives are obligated in Ma'aser after they have grown a third.

Question: What is the source of this?

Answer (Rav Asi) Question: (Hakhel is) "Mi'Ketz Sheva Shanim b'Mo'ed Shenas ha'Shemitah b'Chag ha'Sukos". It is in the eighth year; why is it called Shemitah?

Answer: This teaches that any Tevu'ah that was a third grown before Rosh Hashanah has Kedushas Shemitah.

13b - Rabah: Chachamim said that we follow Chanatah regarding trees.

15b - Beraisa: If Chanatah of fruits was before Tu bi'Shvat, they are tithed like last year. If Chanatah was after Tu bi'Shvat, they are tithed like this year.

R. Nechemyah says, this refers to a tree that produces two yields in a year. If a tree that produces one yield in a year, such as dates, olives and carobs, even if Chanatah was before Tu bi'Shvat, they are tithed like this year.

R. Yochanan: Regarding carobs, people conduct like R. Nechemyah.

Ma'aseros 1:2: When are fruits liable for Ma'aser? For figs, it is when Yivchelu (the ends become white); for grapes when the pits show...

Rishonim

Rambam (Hilchos Ma'aser Sheni 1:2): If fruits reached Onas ha'Ma'aser (sufficient development to obligate tithing) before Tu bi'Shvat of the third year, even if they later were finished and gathered at the end of the year, we take Ma'aser Sheni, like second-year produce. If they reached Onas ha'Ma'aser before Tu bi'Shvat of the fourth year, even if they were gathered at the end of the year, we take Ma'aser Oni, like third-year produce If they reached Onas ha'Ma'aser after Tu bi'Shvat, they are tithed like the current year.

Rambam (3): Even if Chanatah of carobs was before Tu bi'Shvat they are tithed like this year, because their Ma'aser is mid'Rabanan.

Rambam (Hilchos Shemitah v'Yovel 4:9): If Tevu'ah, legumes or fruits reached Onas Ma'aser before Rosh Hashanah of Shemitah they are permitted. Even if they are gathered in Shemitah, they are like sixth year produce in every respect;

If they reached Onas Ma'aser after Rosh Hashanah they are like Shemitah produce.

Question (Tosfos R. Akiva Eiger, Ma'aseros [2] and Rashash Rosh Hashanah 2a DH Sham b'Echad): All over Shas, we say that the year of Ma'aser is determined by Chanatah. Why do the Rambam and Rashi (12b DH veha'Zeisim) say that it depends on Onas Ma'aser?

Note: Elsewhere (12b DH Mina, 14a DH Af Kol and Ho'il), Rashi says that we follow Chanatah.

Answer #1 (Radvaz Ma'aser Sheni 1:2 and Yefe Einayim Rosh Hashanah 15b): The Rambam holds like R. Nechemyah, who does not follow Chanatah before Tu bi'Shvat. Rather, it depends on reaching Onas Ma'aser.

Note: Also the Me'iri (Rosh Hashanah 13b Sof DH ha'Orez) explains the Rambam like this. He agrees, but on 14b (DH Kevar) he says that we follow Chanatah.

Answer #2 (Ri Korkus Ma'aser Sheni 1:1 DH Od Sham (13b) and Mishnah Rishonah Shevi'is 5:1): The Rambam holds that Chanatah is Onas Ma'aser. The Ibn Ezra explains Chanatah (Shir ha'Shirim 2:13) to be when the fruit becomes sweet, or like dust. Rashi says that it is the time for Bikurim to be brought. The Radak says that it is the emerging of fruits before full ripening. These are close to the Rambam's definition. (Rabah taught that we follow Chanatah, i.e. for fruits for which no Shi'ur was taught - Mishnah Rishonah.)

Rebuttal (R. Shlomo Siriliyo, Shevi'is Reish Perek 5 DH v'Ika l'Meiak): The last Mishnah in Perek 4 of Shevi'is forbids cutting a carob tree in Shemitah after Yeshalshelu (the fruits are heavy and hang down). R. Chinena bar Papa says that this is Chanatah. The same Mishnah permits to cut once it reaches Onas Ma'aser! Also, the Yerushalmi in Shekalim compares pregnancy to Chanatah, and birth to one-third growth.

Defense (Chazon Ish Shevi'is 7:12 DH v'Yesh and 7:19 DH uleha'Amor): Chanatah precedes a third growth only for apples and Esrogim. Regarding these, the Yerushalmi compares pregnancy to Chanatah, and birth to one-third growth. Amora'im argue about carobs; the Halachah does not follow R. Chinena bar Papa. The Rambam is able to learn simply that the years of Ma'aser of all fruits depends on Chanatah before Tu bi'Shvat. Tosfos and R. Shimshon (brought below) hold that olives do not follow Chanatah, rather, one-third growth. They must say that olives are an exception, and their year depends on Rosh Hashanah.

Answer #3 (Pnei Yehoshua Rosh Hashanah 12b DH bi'Gmara): The Sugya holds that Kedushas Shemitah of fruits depends on Onas Ma'aser. It must be that Ma'aser of the fruits is mid'Oraisa; if so, surely this also determines the year of Ma'aser. The Rambam holds that this applies to all fruits, for Ma'aser of all fruits is mid'Oraisa. Rashi and Tosfos hold that our Sugya discusses grapes and olives, for which Ma'aser is mid'Oraisa. Regarding other fruits it is mid'Rabanan, and the year of Ma'aser depends on Chanatah.

Question #1: How can the Gemara learn about Onas Ma'aser from Shemitah? Regarding fruits, Shemitah depends on Chanatah, but the Shi'ur for Ma'aser is different. (The Mishnah (Ma'aseros 1:3) gives different Shi'urim for different fruits!)

Answer #1 (Tosfos 12b DH ha'Tevu'ah and R. Shimshon Shevi'is 2:7): Regarding everything else, Ma'aser is determined by when something is fitting. The Gemara knew that Tevu'ah and olives are fitting before one-third growth, therefore it asked why they are exempt until one-third growth. It answered that even regarding Shevi'is we follow one-third growth for them, even though regarding fruits Shemitah depends on Chanatah but Chiyuv Ma'aser comes later, when they grow a third. The Mishnah gives Simanim when this is for different fruits.

Question #2: Why are the years of Ma'aser for fruits determined by Chanatah, but the Chiyuv to take Ma'aser is a different Shi'ur?

Answer #1 (R. Shimshon, ibid.): Except for grapes and olives, Ma'aser of fruits is mid'Rabanan. The Chiyuv Ma'aser is when they are fitting to eat. The years of Ma'aser were patterned after Orlah mid'Oraisa, which depends on Chanatah.

Answer #2 (to both questions - Ri Korkus): These are not difficult for the Rambam. Also regarding fruits, the years of Shemitah and Ma'aser depend on Onas Ma'aser, i.e. Chanatah.

Rashi (15b DH Afilu): Even a small amount of growth is considered Chanatah.

Tosfos (Sukah 40a Sof DH ul'Shevi'is): Regarding an Esrog, perhaps a k'Zayis is required to be considered Chanatah.

Rashi (Bamidbar 17:23): "Va'Yatzetz Tzitz" is Chanatah of the fruit, when the flower falls off.

Me'iri (Rosh Hashanah 2a): Some say that Chanatah is budding of flowers. This is wrong. It says (15b) 'trees that were Chonet their fruits'. Rather, it is sprouting of small fruits. Grapes and olives are different, for their Ma'aser is mid'Oraisa.

Poskim

Shulchan Aruch (YD 331:125): If fruits reached Onas ha'Ma'aser before Tu bi'Shvat of the third year, even if they later were finished and gathered at the end of the year, we take Ma'aser Sheni, like second-year produce. If they reached Onas ha'Ma'aser before Tu bi'Shvat of the fourth year, even if they were gathered at the end of the year, we take Ma'aser Oni, like third-year produce If they reached Onas ha'Ma'aser after Tu bi'Shvat, they are tithed like the current year.